Regression Analysis Using SPSS - Analysis, Interpretation, and Reporting

Regression analysis is a statistical method for quantifying how well one outcome (the dependent variable) can be predicted or explained by one or more predictors (independent variables), including how much variation in the outcome the predictors account for. It matters because it turns messy relationships—like whether advertising drives sales or whether leadership affects well-being—into testable equations with interpretable coefficients and significance tests.

The core distinction is between correlation and regression. Correlation focuses on whether two variables move together, using a correlation coefficient to describe relationship strength. Regression instead separates roles: the dependent variable is the outcome being predicted, while independent variables are the inputs used to generate an equation. That equation produces a regression coefficient (and an intercept), along with inferential statistics such as t values and overall model tests. In practice, regression also includes an error term to represent influences on the dependent variable not captured by the predictors.

Two main forms are emphasized. Bivariate regression uses exactly one independent variable to predict one dependent variable, making it especially common when the goal is prediction from a single predictor. Multiple regression expands this to three or more variables, typically one dependent variable plus several independent variables, allowing researchers to estimate the unique contribution of each predictor while still assessing the overall model.

The transcript walks through realistic scenarios where regression fits: a marketing manager testing whether price reductions affect sales; an HR department predicting training efficiency from academic performance, leadership ability, and IQ; a social activist examining whether female literacy influences the age of marriage; and a life-satisfaction example where self-esteem, optimism, and perceived control are evaluated as predictors. In each case, the method estimates how much of the outcome’s variance can be accounted for by the chosen predictors.

A key reporting framework is introduced through the regression equation: a constant (B0) representing expected outcome when predictors are zero, a beta coefficient (B1, etc.) representing the change in the dependent variable for a one-unit change in a predictor, and an error term capturing unmeasured factors. Interpretation then relies on several output metrics. The regression coefficient reflects the strength of prediction; unstandardized coefficients are used directly in the regression equation, while standardized beta coefficients (measured in standard deviations) support comparisons across predictors. Model fit is summarized with R and R square, where R square represents the proportion of variance in the dependent variable explained by the predictors. Because R square can look inflated with more predictors or larger samples, adjusted R square is used to correct for that.

An applied example uses SPSS to test whether servant leadership predicts life satisfaction. After running bivariate regression, the model summary reports R square (27.6% variance explained) and an ANOVA significance value (p < .01), supporting a significant effect. The coefficients table provides the standardized beta and a t statistic (t = 9.43) to confirm the predictor’s significance. The reporting approach is then extended to multiple regression with three predictors, where the overall F test and R square increase (58.1% variance explained), and individual predictors are judged using the coefficients table’s t values and p values. The transcript concludes with a practical template: report the hypothesis, regression weights (beta), model fit (R square), and significance (F and p), then repeat for additional hypotheses.